Journal of Algebraic Combinatorics

, Volume 27, Issue 3, pp 317–330 | Cite as

Periodicity of hyperplane arrangements with integral coefficients modulo positive integers

  • Hidehiko Kamiya
  • Akimichi Takemura
  • Hiroaki Terao


We study central hyperplane arrangements with integral coefficients modulo positive integers q. We prove that the cardinality of the complement of the hyperplanes is a quasi-polynomial in two ways, first via the theory of elementary divisors and then via the theory of the Ehrhart quasi-polynomials. This result is useful for determining the characteristic polynomial of the corresponding real arrangement. With the former approach, we also prove that intersection lattices modulo q are periodic except for a finite number of q’s.


Characteristic polynomial Ehrhart quasi-polynomial Elementary divisor Hyperplane arrangement Intersection lattice 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Hidehiko Kamiya
    • 1
  • Akimichi Takemura
    • 2
  • Hiroaki Terao
    • 3
  1. 1.Faculty of EconomicsOkayama UniversityOkayamaJapan
  2. 2.Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan
  3. 3.Department of MathematicsHokkaido UniversityHokkaidoJapan

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